Aspheric coefficients of deformation for a Cartesian oval surface

Abstract

In this paper we propose a mathematical model as a theoretical and practical contribution to the theory of aspheric surfaces, that allows the geometrical calculation of an aspherical refractive surface in cylindrical coordinates \((r,z)\), that correspond to a non-degenerated Cartesian oval of revolution, according to standard formulae [ISO-10110-12 (2007)], including: vertex curvature C, conical constant K and aspheric deformation coefficients \(A_4,\,A_6,\,A_8,\,A_{10}\) and \(A_{14}\). The results are shown for an object and its respective image located at finite distances from the vertex (origin of coordinates) on the optical axis.